Yes. There are an infinite number of ways to do that.
One way is:
(5 pounds north) plus (3 pounds north) plus (8 pounds south).
Two vectors, no; three vectors yes.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
Only if the magnitude of all three vectors equals 0.Suppose three vectors (xi), (xj), (xz) are added. If the above statement is true then adding these three vectors should give a magnitude of x(x2 + x2 + x2)1/2 = xSquaring both sidesx2 + x2 + x2 = x22x2=0The above expression is only solvable for x = 0Hence the answer to the above equation is no, unless both vectors are the zero vector.
Yes, if the three vectors are starting from the same point and are directed at 120 degrees between each two vectors.
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
Two vectors, no; three vectors yes.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
Only if the magnitude of all three vectors equals 0.Suppose three vectors (xi), (xj), (xz) are added. If the above statement is true then adding these three vectors should give a magnitude of x(x2 + x2 + x2)1/2 = xSquaring both sidesx2 + x2 + x2 = x22x2=0The above expression is only solvable for x = 0Hence the answer to the above equation is no, unless both vectors are the zero vector.
Yes, if the three vectors are starting from the same point and are directed at 120 degrees between each two vectors.
Three vectors sum to zero under the condition that they are coplanar (lie in a common plane) and form a triangle. If the vectors are not coplanar, they will not sum to zero. Another way of looking at it is that the sum is zero if any vector is exactly equal in magnitude and opposite in direction to the vector sum (so-called resultant) of the remaining two.
No. Three can, but two need to cancel out exactly, meaning they must have the same magnitude in opposite directions.
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
Yes.
Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.
Two vectors: no. Three vectors: yes.